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How to calculate standard error for a variation

  • Created : Nov, 20, 2019
  • Last Updated : Nov, 21, 2024

AB Testing is an effective method of optimizing your conversion rates. But if repeat the test multiple times, you will tend to see deviations. In this article, we will resolve this issue by calculating the standard error and z-score. The aim of calculating standard error is to know the deviation you can expect from an average conversion rate if you run an experiment multiple times.

You can easily analyze the success and failure of your variation with the help of a standard error and z-score results. Of course, we cannot assume the success or failure of a variation. Also, there is no rocket science behind it. We calculate the possibilities of how successful a variation is. This probability is called Chance to Beat All.

What exactly is Chance to Beat all?

Chance to beat all signifies the probability that your variation will perform better than the control version of your app or website. Remember that CTBA can only be used for multivariate and personalization. Why? Because they apply the frequentist method to calculate the winning version. This means AB Testing and Split URL testing follows a different approach (Bayesian Method ) to calculate the chance to beat all versions.

How to calculate manually the success or failure of your variation :

You can calculate the success or failure of your variation by comparing the results against the control version.

Note: You can change the base for your test at any point in time.

What all key metrics are required in order to ascertain the CTB of a variation :
  • Conversion rates of control version and variation.
  • Chance to beat for a variation.
  • The standard error for the control version and the variant.

How-to-calculate-chance-to-beat-for-a-variation

Let’s know how to calculate the above elements elaboratively :
1. How to calculate the conversion rates of control and variation

Conversion rate is usually defined as the ratio of the number of conversions to the visitors on your website. But it is a binomial random variable while you calculate it mathematically. It means it could have two values. It is signified as variable P.

How can you calculate conversion rates in AB testing :

  • You can determine the value of the P variable by observing ‘n’ visitors on the webpage that you have set out for AB testing. Now, simply calculate the no. of conversions from those ‘n’ visitors. The percentage value you get will be the conversion rate of your website or app.

Conversion rate: Actual conversions divided by the visits to the website.

Let’s take an example :

Say, you are running a test to evaluate the design of your home page. The control version has 785 visitors out of which 425 are converted. The variation, on the other hand, receives 754 visits out of which 420 are converted. These numerical values indicate that the conversion rate of the control version is 54.15 percent and the conversion rate for the variation will be 55 percent.

2. How to calculate the standard error for control and variations

We all tend to repeat the same test innumerable times in order to be sure of the exact conversion rate. If you are doing a similar thing, you will get a different value of P every single time. This occurs due to the fact that a sampling test will never cover an entire population.

You will get a different audience and they will be displaying different behavior as well. Hence, You will observe a range of errors each time you are repeating the test. Therefore in spite of repeating the tests, you can use the existing statistical method to calculate the standard error. By applying the same, you can determine how much deviation from the average conversion rate can be expected from the test results. That is how you can come to the conclusion: if your deviation is smaller then you can be assured of estimating the true conversion rate.

Hence, you can calculate the standard error for a given conversion rate and for the no. of trials as follows :

Standard error = Square root of (p * (1-p )/n )

Standard error for control = Square root of (0.54*( 1-0.54 / 785 ) = 1.7 * 10-2 

Standard error for variation = Square root of (0.55*(1-0.55/754) = 1.8 *10-2

3. How to calculate the CTBA for a variation

We calculate the z-score for control and variation in order to determine the CTB for a variation. A Z-score is used in statistics to represent any normal distribution as a standard normal distribution, where the below values denote the following key metrics :

  • Pv = Conversion rate of variation
  • Pc = Conversion rate of control
  • SEv = Standard error of variation
  • SEc = Standard error of control

How can you derive Z-score : (0.55-0.54 )/square root of 0.017788567 +0.018117652 =   0.05277

Now that we have got the z-score, we can determine the normal distribution value as well.

Now you can easily derive the conversion rates and the standard error of AB Testing results by using the above discussed statistical formula. You can ascertain the key metrics and allow yourself to make significant changes in your marketing campaigns.

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  256. While the solution to today's Wordle is rather popular, it is by no means simple. Not at all. This is little better than the game's average. And as you are undoubtedly aware, words may be difficult, even simple ones. spacebar clicker

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